The construction industry is increasingly facing challenges related to budget overruns, resource inefficiencies, and cost estimation inaccuracies. Predictive analytics, powered by machine learning (ML) techniques, offers a transformative solution to enhance cost management practices in construction projects. This review paper explores the current state and advancements in applying ML algorithms—such as linear regression, decision trees, support vector machines, random forests, artificial neural networks, and XGBoost—for cost prediction and budget control. It highlights practical applications including cost overrun forecasting, budget estimation, resource allocation, and risk analysis. The paper also examines critical challenges such as data quality, model interpretability, scalability, and integration barriers with existing project management systems. Furthermore, it identifies future directions, including the integration of predictive analytics with Building Information Modeling (BIM), Internet of Things (IoT), and digital twins. The findings suggest that despite certain limitations, machine learning holds significant promise for revolutionizing cost management through data-driven and proactive decision-making in the construction sector.